The probability that a basketball player will be thrown into the basket is 0.2.

The probability that a basketball player will be thrown into the basket is 0.2. Determine the probability that having made 8 throws, he will hit 3 times.

A – Event the basketball player will be in the basket 3 times out of 8 shots.
Let n = 8 be the number of throws to the basket;
m = 3 – the number of hits in the basket of 8 throws;
Probability of hitting the basket on a throw:
p = 0.2.
The probability of not getting into the basket: 1 – p = 1 – 0.2 = 0.8;

C (n, m) – number of combinations from n to m;
The probability of event A is calculated using the Bernoulli formula:
P (A) = C (n, m) p ^ m (1 – p) ^ (n – m) =
= C (8.3) 0.2 ^ 3 (1 – 0.2) ^ (8 – 3) =
= 8! / (3! (8 – 3)!) 0.2 ^ 3 0.8 ^ 5 =
= 56 0.2 ^ 3 0.8 ^ 5 = 0.147;
Answer: 0.147.